Problem: Simplify the following expression: $p = \dfrac{n^2 + 7n + 12}{n + 3} $
Solution: First factor the polynomial in the numerator. $ n^2 + 7n + 12 = (n + 3)(n + 4) $ So we can rewrite the expression as: $p = \dfrac{(n + 3)(n + 4)}{n + 3} $ We can divide the numerator and denominator by $(n + 3)$ on condition that $n \neq -3$ Therefore $p = n + 4; n \neq -3$